Question 1194127
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The response from the other tutor shows a partial list of the subsets and then, without explanation, the answer, 64.<br>
That doesn't help the student much in determing HOW to find that the answer is 64.  If there were 10, or 100, elements in the set, you wouldn't want to find the number of subsets by listing all of them.<br>
To see how to get the answer of 64, imagine the process of forming a subset from the 6 elements in the given set.  You look at each of the elements and choose whether or not to include that element in your subset.  That's 2 choices -- Yes or No -- for each element.  With 6 elements, the total number of different subsets you can form is the product of those numbers of choices for all 6 elements, which is 2^6 = 64.<br>
So, in short, the number of subsets of set with n elements is 2^n.<br>
This result can also be seen in Pascal's Triangle.<br>
In forming a subset from a set of 6 elements, you can choose either 0, 1, 2, 3, 4, 5, or 6 of the elements.  So the total number of subsets you can form is<br>
C(6,0)+C(6,1)+C(6,2)+C(6,3)+C(6,4)+C(6,5)+C(6,6)<br>
But those numbers are the entries in the 6th row of Pascal's Triangle; and the sum of the entries in the 6th row of Pascal's triangle is 2^6.<br>
So again we see that the number of subsets of a set with n elements is 2^n.<br>